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#include "tropicaldeterminant.h"
#include <algorithm>
#include "printer.h"
#include "log.h"
using namespace std;
static int sub(int a, int b)
{//a-b
assert(b!=td_minusInfinity);
if(a==td_minusInfinity)return td_minusInfinity;
return a-b;
}
static int max(int a, int b)
{
if(a==td_minusInfinity)return b;
if(b==td_minusInfinity)return a;
if(a>b)return a;
return b;
}
/*
* Computes the tropical max determinant using the Hungarian method.
* The implementation follows notes by Golin on Bipartite matchings.
*/
int tropicalDeterminant(IntegerMatrix const &m_)
{
IntegerMatrix m=m_;
int d=m_.getHeight();
int n=m_.getWidth();
// make a square matrix by introducing zeros
if(d<=n)
{
m=m_;
m.append(IntegerMatrix(n-d,n));
d=n;
}
else
{
m=m_.transposed();
m.append(IntegerMatrix(d-n,d));
n=d;
}
int total=(n*n-n)/2;
IntegerVector labelingRows(d);
IntegerVector labelingColumns(n);
for(int j=0;j<n;j++)
{
int colmax=td_minusInfinity;
for(int i=0;i<d;i++)colmax=max(m[i][j],colmax);
labelingColumns[j]=colmax;
if(colmax==td_minusInfinity)return td_minusInfinity;
}
// choose trivial matching M
IntegerVector M(n);
for(int i=0;i<n;i++)M[i]=-1;
IntegerVector Minv(d);
for(int i=0;i<d;i++)Minv[i]=-1;
while(M.sum()!=total)
{
log3 debug<<"M"<<M<<"\n";
log3 debug<<"Minv"<<Minv<<"\n";
log3 debug<<"Lrows"<<labelingRows<<"\n";
log3 debug<<"Lcolumns"<<labelingColumns<<"\n";
int chosenRow=0;
while(chosenRow<d){if(Minv[chosenRow]==-1)break;chosenRow++;}
log3 debug<<"ChosenRow"<<chosenRow<<"\n";
IntegerVector S(d);//-1=not present, n=root
for(int k=0;k<d;k++)S[k]=-1;
S[chosenRow]=d;
IntegerVector T(n);//-1=not present
for(int k=0;k<n;k++)T[k]=-1;
l:
log3 debug<<"looping\n";
log3 debug<<"T"<<T<<"\n";
log3 debug<<"S"<<S<<"\n";
// compute NLS
IntegerVector NLS(n);
for(int k=0;k<n;k++)NLS[k]=-1;
for(int i=0;i<d;i++)
{
if(S[i]!=-1)
for(int j=0;j<n;j++)
{
if(NLS[j]==-1)if(labelingRows[i]+labelingColumns[j]==m[i][j])NLS[j]=i;
}
}
log3 debug<<"NLS"<<NLS<<"\n";
// find element in difference
int chosenColumn=0;
while(chosenColumn<n)
{
if(NLS[chosenColumn]!=-1 && T[chosenColumn]==-1)
break;
chosenColumn++;
}
log3 debug<<"ChosenCol"<<chosenColumn<<"\n";
if(chosenColumn==n)
{
// if no element in difference then update labels
log3 debug<<"Updating labels\n";
int minusal=td_minusInfinity;
for(int i=0;i<d;i++)if(S[i]!=-1)
for(int j=0;j<n;j++)if(T[j]==-1)
minusal=max(minusal,sub(sub(m[i][j],labelingRows[i]),labelingColumns[j]));
log3 debug<<"M"<<M<<"\n";
log3 debug<<"Minv"<<Minv<<"\n";
log3 debug<<"Lrows"<<labelingRows<<"\n";
log3 debug<<"Lcolumns"<<labelingColumns<<"\n";
log3 debug<<"T"<<T<<"\n";
log3 debug<<"S"<<S<<"\n";
log3 debug<<"Minus al"<<minusal<<"\n";
if(minusal==td_minusInfinity)return td_minusInfinity;//is this right?
for(int i=0;i<d;i++)if(S[i]!=-1)labelingRows[i]+=minusal;
for(int i=0;i<n;i++)if(T[i]!=-1)labelingColumns[i]-=minusal;
log3 debug<<"Lrows"<<labelingRows<<"\n";
log3 debug<<"Lcolumns"<<labelingColumns<<"\n";
goto l;
}
else
{
if(M[chosenColumn]==-1)
{
log3 debug<<"Updating using alternating path\n";
log3 debug<<"T"<<T<<"\n";
log3 debug<<"S"<<S<<"\n";
log3 debug<<"chosenrow"<<chosenRow<<"\n";
// we have found alternating path... update
T[chosenColumn]=NLS[chosenColumn];
// while(n!=S[NLS[chosenColumn]])
while(n!=S[T[chosenColumn]])
{
int c=chosenColumn;
// int b=NLS[c];
int b=T[c];
int a=S[b];
//add path b->c
M[c]=b;
Minv[b]=c;
chosenColumn=a;
}
M[chosenColumn]=chosenRow;
Minv[chosenRow]=chosenColumn;
log3 debug<<"Done updating\n";
}
else
{
int z=M[chosenColumn];
T[chosenColumn]=NLS[chosenColumn];//Minv[z];//or chosen row?
S[z]=chosenColumn;
goto l;
}
}
}
log3 debug<<"M"<<M<<"\n";
int ret=0;
for(int i=0;i<n;i++)
ret+=m[M[i]][i];
return ret;
}
int tropicalDeterminantSlow(IntegerMatrix const &m_)
{
IntegerMatrix m=m_;
if(m.getHeight()>m.getWidth())m=m.transposed();
int d=m.getHeight();
int n=m.getWidth();
int ret=td_minusInfinity;
list<int> perm;
for(int i=0;i<d;i++)perm.push_back(i);
for(int i=d;i<n;i++)perm.push_back(d);
do
{
int prod=0;
int i=0;
for(list<int>::const_iterator I=perm.begin();I!=perm.end();i++,I++)if(*I!=d)
{if(m[*I][i]==td_minusInfinity){prod=td_minusInfinity;break;}prod+=m[*I][i];}
ret=max(ret,prod);
}while(next_permutation(perm.begin(),perm.end()));
return ret;
}
void tropicalDeterminantTest()
{
for(int i=0;i<100000;i++)
{
debug<<i<<"\n";
int d=((unsigned int)rand())%6;
int n=((unsigned int)rand())%6;
IntegerMatrix m(d,n);
for(int y=0;y<d;y++)
for(int x=0;x<n;x++)
{
if(rand()&1)
m[y][x]=td_minusInfinity;
else
m[y][x]=rand()%16;
}
if(tropicalDeterminantSlow(m)!=tropicalDeterminant(m))
{
debug<<m.getRows();
debug<<tropicalDeterminantSlow(m)<<"\n";
debug<<tropicalDeterminant(m)<<"\n";
assert(0);
}
}
}
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